{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Approximating the Lyapunov Exponent of the Lorenz System in NumPy\n",
    "\n",
    "The Lorenz equations are a prototypical example of **deterministic chaos**. They\n",
    "are a system of three **nonlinear** ODEs\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{dx}{dt} &= \\sigma(y - x), \\\\\n",
    "\\frac{dy}{dt} &= x(\\rho - z) - y, \\\\\n",
    "\\frac{dz}{dt} &= xy - \\beta z.\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The three variables can be combined into the state vector $u = (x, y, z) \\in\n",
    "\\mathbb{R}^3$. Assume we have an initial condition $u(0)$ and another one\n",
    "slightly next to it $\\tilde{u}(0)$. Hence, their difference is $\\delta u(0) =\n",
    "\\tilde{u}(0) - u(0)$. The maximum Lyapunov exponent $\\lambda$ describes how\n",
    "(exponentially) quickly the two trajectories diverge\n",
    "\n",
    "$$\n",
    "\\| \\delta u(t) \\| \\approx \\| \\delta u(0) \\| \\exp(\\lambda t).\n",
    "$$\n",
    "\n",
    "\n",
    "In this notebook, we will approximate $\\lambda$ for the Lorenz system under the\n",
    "original configuration $\\sigma = 10$, $\\rho = 28$ and $\\beta = 8/3$ (1) using a\n",
    "[Runge-Kutta 4\n",
    "simulator](https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/simulation_scripts/lorenz_simulator_numpy.ipynb)\n",
    "of time step size $\\Delta t = 0.01$ with the following strategy:\n",
    "\n",
    "1. Draw a reasonable initial condition, e.g. $u^{[0]} = (1, 1, 1)$.\n",
    "2. Evolve the initial condition until it enters the chaotic attractor, e.g., by\n",
    "   using $5000$ time steps to get $u^{[5000]}$.\n",
    "3. Use the last state $u^{[5000]}$ as the \"warmed-up\" initial state $u^{[0]}\n",
    "   \\leftarrow u^{[5000]}$.\n",
    "4. Perturb this \"warmed-up state\" by a small amount, e.g. $\\delta u^{[0]} =\n",
    "   10^{-8} \\odot \\epsilon$ with $\\epsilon_i \\propto \\mathcal{U}(-1, 1)$ to get\n",
    "   $\\tilde{u}^{[0]} = u^{[0]} + \\delta u^{[0]}$.\n",
    "5. Evolve both states simultaneously for a certain number of time steps, e.g.\n",
    "   another 5000 time steps.\n",
    "6. Compute the norm of the difference trajectory $\\|\\delta u^{[t]}\\|_2 =\n",
    "   \\|\\tilde{u}^{[t]}- u^{[t]}\\|_2$ at each time step $t$.\n",
    "7. Find the range of time steps in which the difference is growing\n",
    "   (approximately) exponentially linear (e.g., by visual inspection in a\n",
    "   log-linear plot). It will turn out that using $\\approx 2000$ time steps is\n",
    "   sufficient.\n",
    "8. Fit a linear affine model to the following dataset $\\{ \\{t \\Delta\n",
    "   t\\}_{t=0}^T, \\{ \\log(\\|\\delta u^{[t]}\\|_2) \\}_{t=0}^{2000}\\}$ to approximate\n",
    "   the Lyapunov exponent $\\lambda$.\n",
    "9. (Optional) repeat the process for different initial conditions or different\n",
    "   perturbations and average the found Lyapunov exponents.\n",
    "\n",
    "This notebook is greatly inspired by this [wonderful example of the Chebfun\n",
    "library](http://www.chebfun.org/examples/ode-nonlin/LyapunovExponents.html).\n",
    "\n",
    "---\n",
    "\n",
    "(1) E. N. Lorenz, \"Deterministic Nonperiodic Flow\", Journal of the Atmospheric\n",
    "Sciences, 1963,\n",
    "https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lorenz_rhs(u, *, sigma, rho, beta):\n",
    "    x, y, z = u\n",
    "    x_dot = sigma * (y - x)\n",
    "    y_dot = x * (rho - z) - y\n",
    "    z_dot = x * y - beta * z\n",
    "    u_dot = np.array([x_dot, y_dot, z_dot])\n",
    "    return u_dot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LorenzStepperRK4:\n",
    "    def __init__(self, dt=0.01, *, sigma=10, rho=28, beta=8/3):\n",
    "        self.dt = dt\n",
    "        self.sigma = sigma\n",
    "        self.rho = rho\n",
    "        self.beta = beta\n",
    "    \n",
    "    def __call__(self, u_prev):\n",
    "        lorenz_rhs_fixed = lambda u: lorenz_rhs(\n",
    "            u,\n",
    "            sigma=self.sigma,\n",
    "            rho=self.rho,\n",
    "            beta=self.beta,\n",
    "        )\n",
    "        k_1 = lorenz_rhs_fixed(u_prev)\n",
    "        k_2 = lorenz_rhs_fixed(u_prev + 0.5 * self.dt * k_1)\n",
    "        k_3 = lorenz_rhs_fixed(u_prev + 0.5 * self.dt * k_2)\n",
    "        k_4 = lorenz_rhs_fixed(u_prev + self.dt * k_3)\n",
    "        u_next = u_prev + self.dt * (k_1 + 2*k_2 + 2*k_3 + k_4)/6\n",
    "        return u_next"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "lorenz_stepper = LorenzStepperRK4()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_0 = np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.01256719, 1.2599178 , 0.98489097])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lorenz_stepper(u_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def produce_trj(init, n_steps=5000):\n",
    "    trj = [init,]\n",
    "    u_current = init \n",
    "    for i in range(n_steps):\n",
    "        u_current = lorenz_stepper(u_current)\n",
    "        trj.append(u_current)\n",
    "    trj = np.array(trj)\n",
    "    return trj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "trj = produce_trj(u_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5001, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trj.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_0_warmed = trj[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_0_warmed_noise = u_0_warmed + 1e-8 * (np.random.rand(3) * 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0733389052901085e-08"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(u_0_warmed_noise - u_0_warmed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_warmed_trj = produce_trj(u_0_warmed)\n",
    "u_warmed_noise_trj = produce_trj(u_0_warmed_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "distance_trj = np.linalg.norm(u_warmed_noise_trj - u_warmed_trj, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5001,)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_trj.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(distance_trj)\n",
    "plt.xlabel(\"time step\")\n",
    "plt.ylabel(\"distance norm\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_points = np.arange(len(distance_trj)) * lorenz_stepper.dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9346950260454424"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lyapunov_exponent, log_offset = np.polyfit(time_points[:2000], np.log(distance_trj)[:2000], 1)\n",
    "\n",
    "lyapunov_exponent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to\n",
    "\n",
    "    Viswanath, Divakar. Lyapunov exponents from random Fibonacci sequences to the\n",
    "    Lorenz equations. Doctoral dissertation. Cornell University, 1998.\n",
    "\n",
    "page 74, table (c) the Lyaupnov exponent of the Lorenz system is $\\lambda\n",
    "\\approx 0.9056$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oftentimes the inverse of the Lyapunov exponent, i.e. the Lyapunov time, is used\n",
    "as a time scale for the system. Many people use to measure the extent of\n",
    "predictability of a system, i.e., that after a Lyapunov time the system becomes\n",
    "chaotic.\n",
    "\n",
    "Since the basis for the exponential analysis is $e$, the distance grows by\n",
    "$\\approx 2.71$ after one Lyapunov time $\\bar{t}$. Conversely, this means that\n",
    "after $\\approx 2.3$ Lyapunov times, the distance has grown by one order of\n",
    "magnitude, after $\\approx 4.6 \\bar{t}$ this is two orders of magnitude, and\n",
    "after $\\approx 10 \\bar{t}$ this is approx four orders magnitude.\n",
    "\n",
    "- $t= \\frac{1}{\\lambda}$: distance grows by $e$, i.e., $\\frac{\\| \\delta u^{[t]}\n",
    "  \\|}{\\| \\delta u^{[0]} \\|} \\approx 2.71$.\n",
    "- $t= 2.3 \\frac{1}{\\lambda}$: distance grows by one order of magnitude, i.e.,\n",
    "  $\\frac{\\| \\delta u^{[t]} \\|}{\\| \\delta u^{[0]} \\|} \\approx 10$.\n",
    "- $t= 4.6 \\frac{1}{\\lambda}$: distance grows by two orders of magnitude, i.e.,\n",
    "    $\\frac{\\| \\delta u^{[t]} \\|}{\\| \\delta u^{[0]} \\|} \\approx 100$.\n",
    "- $t= 10 \\frac{1}{\\lambda}$: distance grows by four orders of magnitude, i.e.,\n",
    "    $\\frac{\\| \\delta u^{[t]} \\|}{\\| \\delta u^{[0]} \\|} \\approx 10^4$.\n",
    "- $t= 20 \\frac{1}{\\lambda}$: distance grows by eight orders of magnitude, i.e.,\n",
    "    $\\frac{\\| \\delta u^{[t]} \\|}{\\| \\delta u^{[0]} \\|} \\approx 10^8$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'distance norm')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TRUE_LYAPUNOV_EXPONENT = 0.9056\n",
    "\n",
    "plt.semilogy(time_points[:1000], distance_trj[:1000])\n",
    "plt.grid()\n",
    "plt.vlines(1 * 2.3 * 1/TRUE_LYAPUNOV_EXPONENT, 1e-9, 1e-3)\n",
    "plt.vlines(2 * 2.3 * 1/TRUE_LYAPUNOV_EXPONENT, 1e-9, 1e-3)\n",
    "plt.vlines(3 * 2.3 * 1/TRUE_LYAPUNOV_EXPONENT, 1e-9, 1e-3)\n",
    "plt.plot(\n",
    "    time_points[:1000],\n",
    "    np.exp(log_offset + lyapunov_exponent * time_points[:1000])\n",
    ")\n",
    "plt.xlabel(\"time\")\n",
    "plt.ylabel(\"distance norm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
